To determine if the relation {(5,0), (0,5), (5,1), (1,5)} is a function, we need to apply the definition of a function. A relation is considered a function if every input (or x-value) maps to exactly one output (or y-value).
Let’s analyze the pairs:
- (5,0)
- (0,5)
- (5,1)
- (1,5)
In this relation, the x-value ‘5’ appears in two pairs: (5,0) and (5,1). This means that the same input of ‘5’ produces two different outputs, 0 and 1. Since a function cannot have the same x-value corresponding to multiple y-values, this indicates that our relation does not satisfy the criteria to be a function.
In conclusion, the relation is not a function because the input ‘5’ is associated with more than one output.